Adsorption on Graphene

In this exercise, you will be asked to calculate the adsorption energy of CO molecule on the graphene surface, in an attempt to reproduce a part of the experiments presented in this paper.

Lattice constant optimization

As you have seen in earlier exercises, the actual energy – and therefore also the stress tensor – depends on many parameters, like the selected functional. This means that geometrical parameters like the lattice constant may also vary and therefore need to be optimized first when building a new geometry. While this could be done using CP2K's CELL_OPT run type, optimizing both the lattice/cell constants and the geometry simultaneously, we are going to do it manually here, especially since we can assume that only the lattice constant will actually change.

What we are using to determine the center volume (the volume for which the energy is minimal) is the Birch–Murnaghan equation of state (to be precise: the BM equation integrated over pressure), which links the energy and the volume using the minimal energy $E_0$, the center volume $V_0$, the bulk modulus $B_0$ and its derivative $B_1$:

Use the following input file as a starting point, and an adapted version of the script you documented in a previous exercise to generate a number of input files for different lattice constants and run the respective calculation. A good interval for the fraction of the lattice constant is $0.90-1.10$ with a step size of $0.025$.

Extract the energies and fit $E_0$, $V_0$, $B_0$, $B_1$ using the Birch–Murnaghan EOS and using the new $V0$ determine the lattice constant. Plot your fit.

bc -l <<< "5.6 * 12.3"
# you can also use variables and capture the output again in a variable:
x=1.025
a=$(bc -l <<< "$x * 2.4612")

Replacing numbers (or any text) inside a file and write the changed file to a new file:

a=3.54
sed -e "s|2.4612|$a|g" graphene.inp > "graphene_V-${x}.inp"

Be careful when fitting values for the Birch-Murnaghan EOS: the volume is usually the volume per atom (and the total volume of the cell you can also get from the CP2K output).

CO adsorption on graphene

Adsorb one CO molecule on a graphene 6X6X1 supercell at the top (T), bridge (B) and center (C) sites with oxygen atop the carbon (and both perpendicular to the graphene, the u orientation) and optimize the geometry. See the paper for the definitions as well as initial values for the distances.

You need change the RUN_TYPE to GEO_OPT and also specify the (absolute) coordinates by yourself.

You can get a 6x6x1 unit cell with absolute coordinates by using MULTIPLE_UNIT_CELL for the original/geometry-optimized input file like shown in a previous examples, run it with CP2K and get the calculated absolute coordinates from the CP2K output (you can interrupt the actual calculation since the coordinates are printed before the actual calculation starts):

This means that you also have to run an auxiliary geometry optimization calculation for CO in vacuum, using the same settings as for the other calculations. Use a large enough cell (~ 15 Å) and CENTER_COORDINATES for this.